quasi-likelihood in glm (PR#284)

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Subject: quasi-likelihood in glm (PR#284)
plummer@iarc.fr
Date: Wed 22 Sep 1999 - 19:42:18 EST


Message-Id: <199909220942.LAA16986@pubhealth.ku.dk>

I have been using quasi-likelihood to analyze some overdispersed lesion
count data which requires the variance function "mu^2" (specifically,
I am using glm with the family quasi(var="mu^2", link="log")). Some of
the counts are zero which led to problems fitting the model in R.

1) glm was unable to find starting values
2) after I supplied initial values from the fit of a Poisson
   model, glm could not proceed because the deviance was infinite.

Splus 5.0 had no problems fitting the model. I was able to
reproduce the Splus results by editing the quasi() family
generator and using the unnormalized quasi-likelihood

- log(mu) - y/mu (*)

in place of the normalized version

log(y/mu) - (y - mu)/mu (**)

Further investigation of Splus shows how it overcomes these
two problems
1) A fudge factor (in this case 0.167) is added to zero observations
   so that they can be used as starting values.
2) The contribution to the deviance is (*) for zero observations
   and (**) for the rest.

I suggest that R also uses this approach for quasi-likelihood
models.
Martyn

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